The Quantity Theory of Money.

     The most important feature of this theory is that it suggest that interest rates have no effect on the demand for money.

 Velocity of Money and the Equation of Exchange.

 A - Velocity of Money. The value of turnover of money, i.e., the average number of times per year that a KD is spent in buying the total amount of goods and services produced in the economy:

 V = P.Y / M.

 multiplying both sides by M we obtain the equation of exchange, which relates nominal income to the quantity of money and velocity.

 M . V = P . Y ( the equation of exchange )

 i.e., the quantity of money multiplied by the number o times this money spent in a given year must equal nominal income.

 B - The Quantity Theory of Money: According to the theory, velocity is constant in the short run. Moreover, classical economists thought that wages and prices were completely flexible and that  the aggregate level of output produced in the economy ( Y ) would remain at the full employment level, i.e., constant in the short run.

      The quantity theory of money then implies that if M doubles, since V and Y are constant, P also must double e.g.,

 if P.Y = 5 billion, while M = 1 billion, then

 V = 5/1= 5.

 if Money supply doubles to 2 billion, the price level must also double and

 P.Y = 2 ´ = 10 billion

 RESULT: for classical economists, the quantity theory of money provided an explanation of movements in the price level: Movements in the price level result solely from changes in the quantity of money.


The Quantity Theory of Money Demand.

 Look at the equation of exchange;

 M . V = P . Q.

     If we divide both sides by V we get

 M = 1 / V . P . Q         or,


 where k is constant, since V is constant.

     Hence the level of transactions determines the quantity of money that people demand.

      Therefore, Fisher’s theory of money suggests that the demand for money is purely a function of income and interest rates have no effect on the demand for money. The demand for money is determined by:

 n the level of nominal income ( P.Y )

 n  the institutions in the economy that affect the way people conduct transactions which determine velocity and hence, k.


The Cambridge Approach to Money Demand.

     The Cambridge economists asked how much money individuals would want to hold. They recognized that money has two properties that motivate people to hold it.

  n Money functions as a medium of exchange that people can use o carry out transactions, i.e., the demand for money would be related to the level of transactions.

  n Money functions as a store of wealth: the level of people’s wealth also affects the demand for money. As individuals wealth grows, they need to store it. Money is one of the assets.

     They concluded that the demand for money would be proportional to nominal income and expressed the demand for money function as;


      This equation looks like Fisher’s money demand equation. However, it does not mean that the Cambridge group agreed with Fisher that interest rates play no role in the demand for money.

       The Cambridge group approach allows individuals to choose how much money they want to hold. Hence Cambridge approach emphasized individuals choice and did not rule out effects of interest rates.


Keynes’ Liquidity Preference Theory.

     Keynes abandoned the classical view that velocity is constant an developed a theory of money that emphasized the importance of interest rates. He called it Liquidity Preference Theory.

     Keynes postulated that there are three motives behind the  demand for money:

1 - The Transactions Motive: Individuals are assumed to hold money because it is a medium of exchange that can be used carry out every day transactions. This demand is primarily determined by the level of people’s transactions. Since transactions are proportional to income, the transactions demand for money is also proportional to income.

2 - The Precautionary Motive: people hold additional money as a cushion against an unexpected need, e.g., a major car repair, hospitalization, … etc.. This demand for money is also determined by the level of transactions they expect to make in the future which are proportional to income. Hence this demand is proportional to income.

3 - The Speculative Motive: Keynes agreed with the classical Cambridge economists that money is a store of wealth and called this motive for holding money the speculative motive. Keynes divided assets that can be used to store wealth into two categories: Money and Bonds. He then asked, why would individuals decide to hold their assets in the form of money rather than bonds?

    People would hold money if its expected return is higher than the expected return on bonds.

    Keynes assumed that that the expected return on money is zero, while the expected retrun on bonds are:

 n the interest payment

 n the expected rate of capital gain.

     There is a negative relationship between interest rates and the price of bonds. If interest rates are expected to increase people will prefer to hold money rather than bonds and vice versa.

    Keynes assumed that there is a normal level of interest rate, below it people will prefer to hold money rather than bonds to avoid any capital loss in the future when interest rates increased.

     If interest is below that normal level, people will prefer to hold their wealth in money, not bonds to avoid any capital loss if interest rate declined in the future, and vice versa.

RESULT; money demand in negatively related to interest rate levels.


Putting the Three Motives Together.

Keynes distinguished between nominal quantities and real quantities of money. People want to hold a certain amount of real money balances which is related to real income ( Y ) and interest rates ( i ) :

    The liquidity preference function means that the demand for real money balances is negatively related to interest rates ( i ) and positively related to real income.

The liquidity preference can be written as

P / M = 1/ f( i, Y ).

multiply both sides by Y

P.Y / M = Y / f( i, Y ).

if ( i ) increases, f ( i, Y ) declines ( money demand ) and therefore velocity rises. Velocity also will change with expectations about future normal levels of interest rates. Hence, Keynes rejected the view that velocity could be treated as constant.


Further Developments in the Keynesian Approach.

1 - The Transactions Demand.

    Baumol and Tobin developed similar demand for money models which demonstrated that even money balances held for transactions purposes are sensitive to the level of interest rates.

    Suppose that Ali  receives KD 1000 at the begining of the month and spend it on transactions, i.e., by the begining of each month he will have KD 1000 and by the end of the month he will have zero. His holdings of money will be KD 500 ( 1000+0/2). He will have KD 12000 per year and since his holdings of money are 500 on average, then the velocity of money V=P.Q/M = 12000/500=24. ( see firgure ( 1 ) below. Suppose that Ali realises that he can hold part of the money balances in cash and the rest in interest bearing assets ( bonds ). So at the begining of the month he will receive 1000, he will hold 500 cash and buy a bond by the other 500. He will start spending under the middle of the month when cash balances drop to zero. He then sell his bonds and get cash of 500 to spend them in the next 15 days until his balances drop to zero. This process contiues each month. The net result is that his average balances 500/2=250. Velocity is then doubled to 12000/250=48.

Figure (1)

     Suppose that the interest rate is 1% per month, then his interest would be

500 x 1/2 x 1% = KD 2.5.

 figure (2)

      Of course he would be better if he holds KD 333.33 and buys KD 666.667 bonds. and his average cash balances would be 333.333/2=167.67, and more better if he holds KD 250 cash and 750 bonds. etc.. The less cash he is holding the more bonds he buys he will earn more interest. But remember that in order to buy and sell bonds Ali will have to pay brokerage fees, and make more trips to the bank or the stock market. Hence  fees  plus  the   time  cost is his transactions

cost. Ali must strike a balance between the return that he will have and the costs that he will pay ( including the time ). If the rate of interest is high, the benefits of bonds will be high, and vice versa.

     The conclusion of Baumol-Tobin is that:

As the interest rates increase, the amount of cash held for transactions purposes will decline, which in turn means that the velocity increases as interest rate increase. In another way:


       The basic idea is that there is an opportunity cost of holding money ( the interest that can be earned on other assets) and there is benefits of money; the avoidance of transactions costs. When interest rate incereases we will try to economize on our holdings of money for transactions costs since the opportunity costs will be high. Hence the transactions demand for money is sensitive to interest rates.

 Precautionary Demand

       Similar to the transactions demand, as interest rates increase rise, the opportunity costs of holding precuationary balances rises, and so the holdings of these money money balances fall. Hence:


Friedman’s Modern Quantity Theory of money.

     Instead of analyzing the specific motives for holding money, friedman simply stated that the demand for money must be influenced by the same factors that influence the demand for any other asset. He applied the theory of asset demand to money. The demand for real money balances is as follows:


 = Permanent income

 = the expected return on money

 = the expected return on bonds

 = the expected return on equities

 = the expected inflation rate


Distinguishing Between Friedman and Keynes’ Theories.

    There are several differences between Friedman’s and the Keynesian’s theory.

 n Friedman recognized that more than one interest rate is important to the operation of aggregate economy. Keynes lumped financial assets other than money in one big category “ Bonds “.

  n  Friedman viewed money and goods are substitutes, that is people choose between them when deciding how much money to hold.

 n Friedman did not take the expected return on money to be constant as did Keynes.

 n Unlike Keynes’s theory, which indicates that interest rates are important determinant of the demand for money, Friedman’s theory suggests that changes in interest rates should have little effect on the demand for money.    According to Friedman, the demand for money is insensitive to interest rates.      Also Friedman’s money demand function is essentially depend on the     permanent income.

 n Friedman stressed the stability the stability of the demand for money function.

     Friedman’s theory is simply a restatement of the quantity theory of money.